So when up against the zero bound, the central bank needs to borrow directly to the state in order to further lower real interest rates?

If you insist on using open market operations in government bonds to conduct your interest rate policy, yes. Then the CB will have to buy tsys until the interest rate on tsys drops to where the CB wants it to be. This is what QE does for you.

But the CB doesn't have to do this by buying and selling tsys (though if the CB actively refuses to treat tsys at least as well as private bonds, or to lend directly to the state on the same terms it offers private banks for rediscounting tsys, you will most likely have a constitutional crisis on your hands).

The CB can simply offer private banks the option to borrow at longer maturities against suitable collateral. This is what LTRO would do for you if it had not been a one-off event. And the CB can offer banks longer maturity deposit facilities. This is already routine in the Eurosystem.

What happens today is that the bank grants you a mortgage, and then it posts the mortgage as collateral with the CB for an overnight loan (neglecting the interbank market, which can be done without loss of generality under an interest rate targeting CB). Instead of this, the CB can offer to let the bank post the mortgage as collateral for a loan with the same maturity as the mortgage. Basically, the CB can offer the bank a fixed-rate loan, as opposed to the variable-rate loan it gets today.

- Jake

If you only spend 20 minutes of the rest of your life on economics, go spend them here.